Originally Posted by

**DamenFaltor** Hello, I am working on a problem in my homework where I need to prove that the identity equation is true. The parameters are, however, that I must only work on one side of the equation. The Equation:

$\displaystyle sec^2x + csc^2x = sec^2x*csc^2x$

I chose the left side to work in. First, using Pythagorean Identity, expand sec and csc:

$\displaystyle (1+tan^2x) + (1+cot^2x)$

Combine the constants:

$\displaystyle tan^2x + cot^2x + 2$

Use the co-function identities to expand again:

$\displaystyle sin^2x/cos^2x + cos^2x/sin^2x + 2/2$

Here is where I think I am stuck, or maybe I took a wrong turn before this. I could go further, and break the sin into its Pythagorean identity:

$\displaystyle (1-cos^2x)/cos^2x + cos^2x/(1-cos^2x) + 2/2$

But then what? No common denominator. I could take the reciprocal of the second term and then add, but it doesn't get me much.

$\displaystyle (1-cos^2x)/cos^2x + (1-cos^2x)/cos^2x + 2/2 $

Brings up

$\displaystyle (2-cos^2x)/cos^2x$

This equals 1, but then I still have that 2/2 to add in, so then I get 3. which is not what $\displaystyle sec^2x*csc^2x$ is.

Where have I gone wrong? (if I've posted this incorrectly, I'll edit it until I get it right. Please forgive any incorrect formatting. This is my first time here.)